Prove that a symmetric matrix has real eigenvalues and that the eigenvectors corresponding to distinct eigenvalues are mutually orthogonal. Use this fact to prove that any symmetric matrix A can be spectrally decomposed into CDC’ with D a diagonal matrix containing the eigenvalues and C the normalized eigenvectors arranged column-wise.

Prove that a symmetric matrix has real eigenvalues and that the eigenvectors corresponding to distinct eigenvalues are mutually orthogonal. Use this fact to prove that any symmetric matrix A can be spectrally decomposed into CDC’ with D a diagonal matrix containing the eigenvalues and C the normalized eigenvectors arranged column-wise.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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